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Metrics, Norms, Inner Products, and Operator Theory by Christopher Heil (Hardcover, 2018)

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Many important topics that are rarely presented in an accessible way to undergraduate students are included, such as unconditional convergence of series, Schauder bases for Banach spaces, the dual of lp topological isomorphisms, the Spectral Theorem, the Baire Category Theorem, and the Uniform Boundedness Principle.